Mathematics – Statistics Theory
Scientific paper
2007-12-06
Annals of Statistics 2007, Vol. 35, No. 5, 2261-2286
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/009053607000000226 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst
Scientific paper
10.1214/009053607000000226
We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of $l_0$-type penalties. The penalties are associated with various choices of the prior distributions $\pi_n(\cdot)$ on the number of nonzero entries of $\mu$ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule which accommodates many of the known thresholding and model selection procedures as particular cases corresponding to specific choices of $\pi_n(\cdot)$. Furthermore, they achieve optimality in a rather general setting under very mild conditions on the prior. We also specify the class of priors $\pi_n(\cdot)$ for which the resulting estimator is adaptively optimal (in the minimax sense) for a wide range of sparse sequences and consider several examples of such priors.
Abramovich Felix
Grinshtein Vadim
Pensky Marianna
No associations
LandOfFree
On optimality of Bayesian testimation in the normal means problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On optimality of Bayesian testimation in the normal means problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On optimality of Bayesian testimation in the normal means problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-91697